- The emerging zoo of second-order set theories
This is a talk at the Young Researchers’ Workshop: Forcing and Philosophy, University of Konstanz, January 18, 2018.

- Virtual large cardinal principles
This is a talk at the Harvard Logic Colloquium, Cambridge, November 8, 2017.

- Filter games and Ramsey-like cardinals
This is a talk at the CUNY Set Theory Seminar, October 20, 2017.

- A model of second-order arithmetic with the choice scheme in which $\Pi^1_2$-dependent choice fails
This is a talk at the Kurt Gödel Research Center Research Seminar in Vienna, Austria, May 18, 2017.

- Computable processes which produce any desired output in the right nonstandard model
This is a talk at the special session “Computability Theory: Pushing the Boundaries” of 2017 AMS Eastern Sectional Meeting in New York, May 6-7.

- Virtual Set Theory and Generic Vopěnka’s Principle
This is a talk at the VCU MAMLS Conference in Richmond, Virginia, April 1, 2017.

- A countable ordinal definable set of reals without ordinal definable elements
This is a talk at the CUNY Set Theory Seminar, February 10, 2017.

- A set-theoretic approach to Scott’s Problem
This is a talk at the National University of Singapore Logic Seminar, October 19, 2016.

- Generic Vopěnka’s Principle at YST2016
This is a talk at the Young Set Theory 2016 Conference in Copenhagen, Denmark, June 13-17, 2016.

- Generic Vopěnka’s Principle
This is a talk at the Rutgers Logic Seminar in New Jersey, May 2, 2016.

- Computable processes can produce arbitrary outputs in nonstandard models
This is a talk at the CUNY MOPA Seminar in New York, April 13, 2016.

- Virtual large cardinals
This is a talk at Set Theory Day in New York, March 11, 2016.

- Ehrenfeucht principles in set theory
This is a talk at the British Logic Colloquium in Cambridge, UK, September 2-4, 2015.

- Indestructible remarkable cardinals
This is a talk at the 5th European Set Theory Conference in Cambridge, UK, August 24-28, 2015.

- An introduction to nonstandard models of arithmetic
This is a talk at the Virginia Commonwealth University Analysis, Logic and Physics Seminar, April 24, 2015.

- Remarkable Laver functions
This is a talk at the CUNY Set Theory Seminar, February 27, 2015.

- Kelley-Morse set theory and choice principles for classes
This is a talk at the SoTFoM II (Symposia on the Foundations of Mathematics) conference in London, UK, January 12-13, 2015.

- Choice schemes for Kelley-Morse set theory
This is a talk at the Colloquium Logicum Conference in Munich, Germany, September 4-6, 2014.

- Incomparable $\omega_1$-like models of set theory
This is a talk at the Connecticut Logic Seminar, March 31, 2014.

- Introduction to remarkable cardinals
This is a talk at the CUNY Set Theory Seminar, March 14, 2014.

- Ramsey cardinals and the continuum function
This is a talk at the CUNY Logic Workshop, February 14, 2014.

- A Jonsson $\omega_1$-like model of set theory
This is a talk at the CUNY Set Theory Seminar, November 15, 2013.

- Embeddings among $\omega_1$-like models of set theory
This is a talk at the CUNY Set Theory Seminar, October 4, 2013.

- Models of $\rm{ZFC}^-$ that are not definable in their set forcing extensions
This is a talk at the CUNY Set Theory Seminar, May 4, 2012.

- Julia sets and the Mandelbrot set
This is a talk at the City Tech Math Club, April 19, 2012.

- Indestructibility for Ramsey cardinals
This is a talk at the Rutgers Logic Seminar, April 2, 2012.

- An iPhone app for a nonstandard model of number theory?
This is a talk at the City Tech C-LAC (Center for Logic, Algebra, and Computation) Seminar, February 14, 2012.

- Forcing and gaps in $2^\omega$
This is a talk at the CUNY Set Theory Seminar, December 2nd, 2011.

- A natural model of the multiverse axioms
This is a talk at the MIT Logic Seminar, April 8, 2010.

- Gödel’s Proof
This is a talk at the United States Military Academy at West Point Mathematics Seminar, January 20, 2010.

- Making strong cardinals indestructible by $\leq\kappa$-weakly closed Prikry forcing
This was a talk at the CUNY Set Theory Seminar sometime in 2009.

### Recent Writing

### Mathoverflow Activity

- Comment by Victoria Gitman on Consistency strength of the existence of a transitive model of $\mathsf{ZFC}^-$ with a $\kappa$-complete ultrafilterAli, I am just seeing the comment because I have been away from MO for a while. So you are saying that even an ill-founded ultrapower by a non-normal filter as long as it is weakly amenable can be used to show that kappa is weakly compact in M?Victoria Gitman
- Answer by Victoria Gitman for Consistency strength of the existence of a transitive model of $\mathsf{ZFC}^-$ with a $\kappa$-complete ultrafilterLet's make some additional assumptions on the ultrafilter $U$. Suppose $M\models{\rm ZFC}^-$ and $\kappa$ is a cardinal in $M$. We say that $U$ is an $M$-ultrafilter if $\langle M,\in,U\rangle$ satisfies that $U$ is a $\kappa$-complete normal ultrafilter on $\kappa$. Because $U$ is only $\kappa$-complete for sequences in $M$ and $M$ might be missing even countable […]Victoria Gitman
- Comment by Victoria Gitman on Consistency strength of the existence of a transitive model of $\mathsf{ZFC}^-$ with a $\kappa$-complete ultrafilterDo you require that the ultrapower is well-founded? Also, do you want $M$ to satisfy that the ultrafilter is normal?Victoria Gitman

- Comment by Victoria Gitman on Consistency strength of the existence of a transitive model of $\mathsf{ZFC}^-$ with a $\kappa$-complete ultrafilter
### Cantor’s Attic

- User:MkortinkUser account Mkortink was createdMkortink
- User:Julian Barathieu← Older revision Revision as of 11:23, 15 March 2018 Line 3: Line 3: For those interested, there is a discord server created by me and [[User:Zetapology|Zetapology]]: https://discord.gg/tbGrU39 For those interested, there is a discord server created by me and [[User:Zetapology|Zetapology]]: https://discord.gg/tbGrU39 −My "ideal background theory" (or just "prefered theory") is $\text{ZFC + GCH + […]Julian Barathieu

- User:Mkortink